The batting Wang Xiu Ying uses to fill quilts has a thermal conductivity rate of $0.03$ watts $(\text{W})$ per meter $(\text{m})$ per degree Celsius $(^\circ\text{C})$. What is the batting's thermal conductivity value in $\dfrac{\text{W}}{\text{cm}\cdot^\circ\text{C}}$ ?
Explanation: We will convert $0.03\,\dfrac{\text{W}}{\text{m}\cdot^\circ\text{C}}$ to a thermal conductivity rate in $\dfrac{\text{W}}{\text{cm}\cdot^\circ\text{C}}$ using the following conversion rate: There are $100\text{ cm}$ per $1\text{ m}$. $\begin{aligned} &\phantom{=} \dfrac{0.03\text{ W}}{1\text{ m}\cdot^\circ\text{C}} \cdot\dfrac{1\text{ m}}{100\text{ cm}} \\\\ &=\dfrac{0.03\cdot1\cdot\text{W}\cdot\cancel{\text{m}}}{1\cdot100\cdot\cancel{\text{m}}\cdot\text{cm}\cdot ^\circ\text{C}} \\\\ &=\dfrac{0.03}{100}\,\dfrac{\text{W}}{\text{cm}\cdot^\circ\text{C}} \\\\ &=0.0003\,\dfrac{\text{W}}{\text{cm}\cdot^\circ\text{C}} \end{aligned}$ In conclusion, the thermal conductivity rate in $\dfrac{\text{W}}{\text{cm}\cdot^\circ\text{C}}$ is: $0.0003\,\dfrac{\text{W}}{\text{cm}\cdot^\circ\text{C}}$